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The Practice of Statistics for AP Examination

Daren Starnes, Josh Tabor

$Math Studyset Vaia Explanations$ Math

6th Edition · 837 pages

ISBN: 9781319113339

Chapter 7: Q.AP2.21 - Cumulative AP Practise Test (page 438)

A large company is interested in improving the efficiency of its customer service and decides to examine the length of the business phone calls made to clients by its sales staff. Here is a cumulative relative frequency graph from data collected over the past year. According to the graph, the shortest $80 %$ of calls will take how long to complete?
a. Less than 10 minutes
b. At least 10 minutes
c. Exactly 10 minutes
d. At least $5.5$ minutes
e. Less than $5.5$ minutes

Short Answer

Expert verified

a. Less than 10 minutes

Step by step solution

01

Given Information

02

Explanation for correct option

Finding $80 %$ on the $Y$ -axis, sketch a line to the right side until it touches the blue graph. Therefore it is cumulative; everything to the left side would be less than 10 minutes. The value will be 10 minutes therefore the shortest $80 %$ of the call would be less than 10 minutes.

Hence, the correct option is (a)

03

Explanation for incorrect option

b. At least 10 minutes is not the answer.

c. Exactly 10 minutes is not the answer.

d. At least 5.5 minutes is not the answer.

e. Less than 5.5 minutes is not the answer.

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Most popular questions from this chapter

Healthy Living From a large group of people who signed a card saying they intended to quit smoking, $1000$ people were selected at random. It turned out that $210 (21 %)$ of these individuals had not smoked over the past $6$ months.

According to the U.S. Census, the proportion of adults in a certain county who owned their own home was 0.71. An SRS of 100 adults in a certain section of the county found that 65 owned their home. Which one of the following represents the approximate probability of obtaining a sample of 100 adults in which 65 or fewer own their home, assuming that this section of the county has the same overall proportion of adults who own their home as does the entire county?

a. $(10065) (0.71) 65 (0.29) 35 (\begin{matrix} 100 \\ 65 \end{matrix}) (0.71)^{65} (0.29)^{35}$

b. $(10065) (0.29) 65 (0.71) 35 (\begin{matrix} 100 \\ 65 \end{matrix}) (0.29)^{65} (0.71)^{35}$

c.

$P (z \leq 0.65 - 0.71 (0.71) (0.29) 100) P (z \leq \frac{0.65 - 0.71}{\sqrt{\frac{(0.71) (0.29)}{100}}})$

d. $P (z \leq 0.65 - 0.71 (0.65) (0.35) 100) P (z \leq \frac{0.65 - 0.71}{\frac{(0.65) (0.35)}{\sqrt{100}}})$

e. $P (z \leq 0.65 - 0.71 (0.71) (0.29) 100) P (z \leq \frac{0.65 - 0.71}{\frac{(0.71) (0.29)}{\sqrt{100}}})$

When people order books from a popular online source, they are shipped in boxes.

Suppose that the mean weight of the boxes is 1.5 pounds with a standard deviation of 0.3 pound, the mean weight of the packing material is 0.5 pound with a standard deviation of 0.1 pound, and the mean weight of the books shipped is 12 pounds with a standard deviation of 3 pounds. Assuming that the weights are independent, what is the standard deviation of the total weight of the boxes that are shipped from this source?

a. 1.84

b. 2.60

c. 3.02

d. 3.40

e. 9.10

The number of undergraduates at Johns Hopkins University is approximately 2000 , while the number at Ohio State University is approximately 60,000. At both schools, a simple random sample of about $3 %$ of the undergraduates is taken. Each sample is used to estimate the proportion p of all students at that university who own an iPod. Suppose that, in fact, p=0.80 at both schools. Which of the following is the best conclusion?

a. We expect that the estimate from Johns Hopkins will be closer to the truth than the estimate from Ohio State because it comes from a smaller population.

b. We expect that the estimate from Johns Hopkins will be closer to the truth than the estimate from Ohio State because it is based on a smaller sample size.

c. We expect that the estimate from Ohio State will be closer to the truth than the estimate from Johns Hopkins because it comes from a larger population.

d. We expect that the estimate from Ohio State will be closer to the truth than the estimate from Johns Hopkins because it is based on a larger sample size.

e. We expect that the estimate from Johns Hopkins will be about the same distance from the truth as the estimate from Ohio State because both samples are 3 % of their populations.

What does the CLT say? Asked what the central limit theorem says, a student replies, "As you take larger and larger samples from a population, the histogram of the sample values looks more and more Normal." Is the student right? Explain your answer.

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